Rance-
Check for link lights on your computer and on the router. You may have a bad ethernet cable, and that's a lot cheaper to fix than a bad router.
I don't know how XBOXes work because I've never networked one. But. Are you hooking them up inside your router, or are you taking out the router to hook up your XBOXes?
If you hook up the XBOX behind the router, and the XBOX gets a network address from the router, then the problem is not the router. It's most likely a network card or software problem on your computer.
If it does turn out to be the router, try unplugging the router's power and plugging it back in, then try to get an address on your computer. If that doesn't do it, perform a factory reset by finding the router's reset switch and holding it in for at least 10 seconds (while power is plugged in). (Routers vary on the factory reset procedure. I think 10 seconds is the right one for Linksys, but check the manual for your specific router.) That will clear out all of the stored settings in the device and replace them with the factory defaults.
If the factory reset still doesn't do it, try assigning your computer a static IP in the default address range. For Linksys, that should be 192.168.1.x, so make your computer 192.168.1.2, then try to get into your router configuration by browsing to
http://192.168.1.1. Roll back the firmware to an earlier version, preferably the one that you just replaced, if you remember what it was.
I have a Linksys 4-port router and a separate wireless-B access point. They can be finicky after firmware upgrades, but the factory reset *should* take care of it.